medians for degree measurements

Terry Reedy tjreedy at
Sat Jan 23 09:20:24 CET 2010

On 1/23/2010 1:09 AM, Steve Howell wrote:
> On Jan 22, 5:12 pm, MRAB<pyt... at>  wrote:

> I like this implementation, and it would probably work 99.9999% of the
> time for my particular use case.  The only (very contrived) edge case
> that I can think of is when you have 10 bearings to SSW, 10 bearings
> to SSE, and the two outliers are unfortunately in the NE and NW
> quadrants.  It seems like the algorithm above would pick one of the
> outliers.
> Maybe the refinement to the algorithm above would be to find the mean
> first, by summing sines and cosines of the bearings, taking the
> quotient, and applying the arctangent.  Then use the resulting angle
> as the equivalent of "due north" and adjust angles to be within (-180,
> 180) respect to the mean, pretty much as you do in the code above,
> with minor modifications.

I was going to suggest this. Let us know if it seems to work.

> I realize the problem as I stated it as sort of ill-defined.

Yes, I think this one reason stat books typically ignore directional 
data. I think it is an unfortunate omission.

Terry Jan Reedy

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